Counting and equidistribution in quaternionic Heisenberg groups

Mixing, counting and equidistribution in Lie groups

Equidistribution and counting for orbits of geometrically finite hyperbolic groups

1.1. Motivation and overview. Let G denote the identity component of the special orthogonal group SO(n, 1), n ≥ 2, and V a finite-dimensional real vector space on which G acts linearly from the right. A discrete subgroup of a locally compact group with finite covolume is called a lattice. For v ∈ V and a subgroup H of G, let Hv = {h ∈ H : vh = v} denote the stabilizer of v in H. A subgroup H of...

Counting Dihedral and Quaternionic Extensions

We give asymptotic formulas for the number of biquadratic extensions of Q that admit a quadratic extension which is a Galois extension of Q with a prescribed Galois group, for example, with a Galois group isomorphic to the quaternionic group. Our approach is based on a combination of the theory of quadratic equations with some analytic tools such as the Siegel–Walfisz theorem and the double osc...

The Heat Kernel and the Riesz Transforms on the Quaternionic Heisenberg Groups

As the heat kernel plays an important role in many problems in harmonic analysis, an explicit usable expression is very much desirable. An explicit expression for the heat kernel for the Heisenberg group Hn = C ×R was obtained by Hulanicki [9] and by Gaveau [7]. Gaveau [7] also obtained the heat kernel for free nilpotent Lie groups of step two. Cygan [4] obtained the heat kernel for all nilpote...

φ-factorable operators and Weyl-Heisenberg frames on LCA groups